Ross-Littlewood Paradox [Image from Steemit website: here. ]
Posts Tagged 'Logic'
The “Napoleon of Crime” and The Laws of Thought
Published November 15, 2018 Irish Times Leave a CommentTags: History, Logic
A fascinating parallel between a brilliant mathematician and an arch-villain of crime fiction is drawn in a forthcoming book – New Light on George Boole – by Des MacHale and Yvonne Cohen. Professor James Moriarty, master criminal and nemesis of Sherlock Holmes, was described by the detective as “the Napoleon of crime”. The book presents convincing evidence that Moriarty was inspired by Professor George Boole [TM151, or search for “thatsmaths” at irishtimes.com].
Continue reading ‘The “Napoleon of Crime” and The Laws of Thought’
“Dividends and Divisors Ever Diminishing”
Published June 14, 2018 Occasional Leave a CommentTags: Arithmetic, Logic
Next Saturday is Bloomsday, the anniversary of the date on which the action of Ulysses took place. Mathematical themes occur occasionally throughout Ulysses, most notably in the penultimate episode, Ithaca, where the exchanges between Leopold Bloom and Stephen Dedalus frequently touch on weighty scientific matters. [Last week’s ThatsMaths post]
Joyce in Zurich: did he meet Zermelo?
Continue reading ‘“Dividends and Divisors Ever Diminishing”’
Enigmas of Infinity
Published March 2, 2017 Irish Times Leave a CommentTags: Analysis, History, Logic
Children sometimes amuse themselves searching for the biggest number. After trying millions, billions and trillions, they realize that there is no end to the game: however big a number may be, we can always add 1 to produce a bigger number: the set of counting numbers is infinite. The concept of infinity has intrigued philosophers since antiquity, and it leads to many surprises and paradoxical results [TM110 or search for “thatsmaths” at irishtimes.com].
The Shaky Foundations of Mathematics
Published December 1, 2016 Irish Times Leave a CommentTags: Algorithms, Logic, Number Theory
The claim is often made that mathematical results are immutable. Once proven, they remain forever valid. But things are not so simple. There are problems at the very core of mathematics that cast a shadow of uncertainty. We can never be absolutely sure that the foundations of our subject are rock-solid [TM104 or search for “thatsmaths” at irishtimes.com].
Left: Plato and Aristotle. Centre: Pythagoras. Right: Euclid [Raphael, The School of Athens]
The ancient Greeks put geometry on a firm footing. Euclid set down a list of axioms, or basic intuitive assumptions. Upon these, the entire edifice of Euclidean geometry is constructed. This axiomatic approach has been the model for mathematics ever since.
The links between mathematics and music are manifold. Mathematics can be set to music in a simple but surprising manner. For the award ceremony of the Gödel Medal in 2014, a musical interpretation of Gödel’s incompleteness Theorems was written by Danish composer Niels Marthinsen. It encodes the basic axioms of number theory that form the focus of Gödel’s Theorems.
The Peano Axioms in symbolic form.
The Year of George Boole
Published December 4, 2014 Irish Times Leave a CommentTags: Algorithms, Computer Science, History, Logic
This week’s That’s Maths column in The Irish Times (TM058, or search for “thatsmaths” at irishtimes.com) is about George Boole, the first Professor of Mathematics at Queen’s College Cork.
